I don't believe it has any long-term parking - just permit parking for locals and metered parking for others - with a max of 24 hours. But I would repost with a specific question about parking at Poughkeepsie metroNorth station (unless you want to take much more expensive Amtrak) that a local familiar with the lot might see. Frequently these stations are full before 8 am with commuters but I don't know this station.
Thank you, I’ll try posting in a different forum,
I am a bit late in posting this but it may be helpful for another time. We have driven to Syracuse from Ottawa and taken the Express bus to NYC. I think you can also catch a train there, but not a commuter train. The bus is very convenient and parking is readily available. Used to be $5 for five days. That may have changed, but probably still pretty good. The bus station in Syracuse is very near the Carousel Mall. The Express bus gets you right downtown in NYC.